Abstract
There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too).
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© 1983 Springer Science+Business Media Dordrecht
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Fitting, M. (1983). Introduction. In: Proof Methods for Modal and Intuitionistic Logics. Synthese Library, vol 169. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2794-5_1
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DOI: https://doi.org/10.1007/978-94-017-2794-5_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8381-4
Online ISBN: 978-94-017-2794-5
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